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Proofgold Proof

pf
Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Apply unknownprop_219a5692ece616b4a88502d80a85b644180cde982b21251f92a23d11d1a5d022 with setminus (binintersect x0 x1) x2, binintersect x0 (setminus x1 x2) leaving 2 subgoals.
Let x3 of type ι be given.
Assume H0: In x3 (setminus (binintersect x0 x1) x2).
Apply unknownprop_e02b92c94ff70655b8eb0623a7ec106c0c0c9c65ac0f52f9689f2e6c9f563b5d with binintersect x0 x1, x2, x3, In x3 (binintersect x0 (setminus x1 x2)) leaving 2 subgoals.
The subproof is completed by applying H0.
Assume H1: In x3 (binintersect x0 x1).
Assume H2: nIn x3 x2.
Apply unknownprop_9f9c1680d203bdbb862d1bf6c2b8504d7e3a6fca72f77bd8968e86ad6ad69346 with x0, x1, x3, In x3 (binintersect x0 (setminus x1 x2)) leaving 2 subgoals.
The subproof is completed by applying H1.
Assume H3: In x3 x0.
Assume H4: In x3 x1.
Apply unknownprop_7e73699eda4c2a35af8db1aea1ddace7d2346405cd3944ace259823e1ec33cf3 with x0, setminus x1 x2, x3 leaving 2 subgoals.
The subproof is completed by applying H3.
Apply unknownprop_3fe7f97dcb00bcf31cf989081bd8403f8f0647acc7dd719f8a7da64cd4837dac with x1, x2, x3 leaving 2 subgoals.
The subproof is completed by applying H4.
The subproof is completed by applying H2.
Let x3 of type ι be given.
Assume H0: In x3 (binintersect x0 (setminus x1 x2)).
Apply unknownprop_9f9c1680d203bdbb862d1bf6c2b8504d7e3a6fca72f77bd8968e86ad6ad69346 with x0, setminus x1 x2, x3, In x3 (setminus (binintersect x0 x1) x2) leaving 2 subgoals.
The subproof is completed by applying H0.
Assume H1: In x3 x0.
Assume H2: In x3 (setminus x1 x2).
Apply unknownprop_e02b92c94ff70655b8eb0623a7ec106c0c0c9c65ac0f52f9689f2e6c9f563b5d with x1, x2, x3, In x3 (setminus (binintersect x0 x1) x2) leaving 2 subgoals.
The subproof is completed by applying H2.
Assume H3: In x3 x1.
Assume H4: nIn x3 x2.
Apply unknownprop_3fe7f97dcb00bcf31cf989081bd8403f8f0647acc7dd719f8a7da64cd4837dac with binintersect x0 x1, x2, x3 leaving 2 subgoals.
Apply unknownprop_7e73699eda4c2a35af8db1aea1ddace7d2346405cd3944ace259823e1ec33cf3 with x0, x1, x3 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H3.
The subproof is completed by applying H4.